101
Views
1
CrossRef citations to date
0
Altmetric
Section A

Vertex-pancyclicity of twisted cubes with maximal faulty edges

Pages 728-740 | Received 17 Jan 2011, Accepted 26 Aug 2011, Published online: 23 Feb 2012
 

Abstract

The n-dimensional twisted cube, denoted by TQ n , a variation of the hypercube, possesses some properties superior to the hypercube. In this paper, we show that every vertex in TQ n lies on a fault-free cycle of every length from 6 to 2 n , even if there are up to n−2 link faults. We also show that our result is optimal.

2010 AMS Subject Classifications::

Acknowledgement

The author is grateful to the National Science Council of the Republic of China, Taiwan for financially supporting this research under Contract No. NSC 98-2221-E-239-013.

Notes

Since , we have 2 n−2 choices. Note that an edge in F can eliminate two choices and . If we cannot find such an edge, then , which is a contradiction when n≥5.

Let and . We have and . Since . We have . Thus, we have (since n≥5). Thus, we can always find such an edge.

Clearly, we have l 0 choices. We can always find such a path since .

Since , we have at least 2 n−1 choices. If such a path does not exist, then when n≥5, which is a contradiction.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.